Maths: Our flawed system

When one looks at maths, one usually thinks of an absolute, a truth, undeniable proofs and facts and calculations. 

We often think of every sum, calculation and equation as unmoving, unchangeable or completely perfect.

For example:
1 + 1 = 2

This is an example of a mathematical FACT. We know its true and we know that the answer cannot be different.


Another example goes a little something like this:
1/3 + 1/3 + 1/3 = 1

Again, mathematical fact. Truth.

BUT wait, what happens if we convert these fractions into the decimal system?
we get this...

0.333.... + 0.333... + 0.333... = 1

And as quickly as that we are met with an obvious flaw.
The answer to this equation Should be 0.999....  right?

OR should it?

The 'truth' is that 1 and 0.999.... are both correct answers to that equation. Not only that, but;

0.9999... IS  1,
(there are various proofs for this, you can search them up if you want.)


But it doesn't make sense!?  
0.999... < 1   
0.999...  = 1
Well, ya just gotta get used to it!  There will be many problems like this when you dive  deeper and deeper into maths, and the fact is that we don't have an absolute answer for everything.

But I think that's good. It gives maths personality, a sense of wonder around it. It reminds us that maths is limited by our minds and cannot go beyond it, since we are the ones to conceptualise it. It reminds us that maths is far from complete, far from perfect and it gives us the motivation and drive to get to as close to perfect as is possible.

BY highlighting this one simple 'flaw' in mathematics I hope I have shown you that maths is a lot more complicated than absolute facts and irrefutable claims. I hope I have shown you that maths is not 'finished' and that there is always more to discover, always more to learn and most of all, there is ALWAYS room for improvement.

Thanks for reading!

HK